Dual point description of mesoscopic superconductors

We present an analysis of the magnetic response of a mesoscopic superconduc tor, i.e., a superconducting sample of dimensions comparable to the coheren ce length and to the London penetration depth. Our approach is based on spe cial properties of the two-dimensional Ginzburg-Landau equations, satisfied at the dual point (kappa = 1/root2). Closed expressions for the free energ y and the magnetization of the superconductor are derived. A perturbative a nalysis in the vicinity of the dual point allows us to take into account vo rtex interactions, using a scaling result for the free energy. In order to characterize the vortex/current interactions, we study vortex configuration s that are out of thermodynamical equilibrium. Our predictions agree with t he results of recent experiments pet-formed on mesoscopic aluminum disks.